Answer:
∠ACB≅∠CAD, Alternate Interior Angles Theorem
∠BAC≅∠DCA, Alternate Interior Angles Theorem
AC≅AC, Reflexive Property of Congruence
By A-S-A congruence, the △ABC≅△CDA.
Step-by-step explanation:
Given the figure:
We are given that:
Side BC || AD
Side AB || DC
Let us have a look at a few properties first.
Alternate Interior Angle Theorem: It states that when two parallel lines are cut by a line then the alternate angles which are on the interior side are equal to each other.
Reflexive Property of Congruence: It states that a side or angle is always congruent to itself.
Now, let us consider the triangles:
△ABC and △CDA.
Side BC || AD
Therefore,
<em>∠ACB≅∠CAD, Alternate Interior Angles Theorem</em>
Side AB || DC
Therefore,
<em>∠BAC≅∠DCA, Alternate Interior Angles Theorem</em>
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Also, Side AC is common.
AC≅AC, Reflexive Property of Congruence
Therefore, by <em>A-S-A congruence</em>, the △ABC≅△CDA.
